In this paper, we study ternary optimal formally self-dual codes. Bounds for the highest minimum weight are given for length up to 30 and examples of optimal formally self-dual codes are constructed. For some lengths, we have found formally self-dual codes which have a higher minimum weight than any self-dual code. It is also shown that any optimal formally self-dual [10, 5, 5] code is related to the ternary Golay code of length 12.
